Question

How do you find the exact value `cos(x-y)` if `cosx=3/5,cosy=4/5`?

Answer 1

`24/25`

Explanation:

Use trig identity:
cos (x - y) = cos x.cos y + sin x.sin y
We have cos x = 3/5, find sin x
We have cos y = 4/5, find sin y
`sin x = 1 - cos^2 x = 1 - 9/25 = 16/25` --> `sin x = +- 4/5`
`sin y = 1 - cos^2 y = 1 - 16/25 = 9/25` --> `sin y = +- 3/5`
Since cos x > 0 and cos y > 0, then the arcs x and y are both located in Quadrant I. Their sin are both positive. There for:
`cos (x - y) = (3/5)(4/5) + (4/5)(3/5) = 24/25`